Zigzag Transition Research Articles

Straight to zigzag transition of foam pseudo-Plateau borders on textured surfaces

Straight to zigzag transition of foam pseudo-Plateau borders on textured surfaces

Low-rank approximations for accelerating plane-wave hybrid functional calculations in unrestricted and noncollinear spin density functional theory.

The adaptively compressed exchange (ACE) operator combined with interpolative separable density fitting (ISDF) decomposition has been utilized to accelerate plane-wave hybrid functional calculations for restricted Kohn-Sham density functional theory (DFT), but the neglect of spin degree of freedom has limited its application in the exploration of systems where the spin property of the electron is critical. Herein, we derive the ACE-ISDF formulation for hybrid functional calculations in both unrestricted and noncollinear spin DFT with plane waves and periodic boundary conditions. We proposed an improved ISDF algorithm for the sum of Kohn-Sham orbital pairs to further reduce the computational cost for the spin-noncollinear case. Numerical results demonstrate that these improved ACE-ISDF low-rank approximations can not only significantly reduce the computational time by two orders of magnitude compared with conventional plane-wave hybrid functional calculations but also lead to a good convergence behavior when a moderate rank parameter is set, even for complex periodic magnetic systems. By using these ACE-ISDF approximations, we investigate the electronic and magnetic properties of two-dimensional periodic ferromagnetic semiconductors consisting of triangular zigzag graphene quantum dots and transition metal atoms. Our computational results showcase that hybrid functional calculations in spin DFT can provide not only accurate electronic structures but also accurate magnetic order temperature of ferromagnetic semiconductors compared to local or semilocal functional calculations.

Migration dynamics of an initially spherical deformable bubble in the vicinity of a corner

Three-dimensional numerical simulations are performed to study the migration dynamics of a deformable bubble that is spherical at an initial time near a corner formed by two vertical walls. Near-wall dynamics of this rising bubble are studied by investigating its path, wake, shape and velocity. A finite volume approach coupled with VOF (volume-of-fluid) method is adopted to solve the incompressible Navier–Stokes equation and track the gas–liquid interface. From the study, it is found that bubble inertia is dictated by initial bubble–walls interaction as bubble progressively migrates away in a diagonal direction from both the vertical walls in three-dimensional space. This influenced bubble inertia, in turn, affects the conformity of the bubble to a specific bubble regime. Five regimes are identified based on the bubble's migrating trajectory among which three of them are fully developed-steady, zigzag, and spiral and two of them are transitional-steady to zigzag and zigzag to spiral. The point of complete transformation of bubble from steady to zigzag transition to fully developed path instability is evaluated by varying a certain dimensionless parameter, Galilei number Ga. It is found that the path instability occurs at a lower Ga than what it is for the unbounded situations, and the onset of planar zigzag motion is not the result of vortex shedding rather the critical amount of wake accumulation on bubble surface and bubble inertia modulated by walls. Furthermore, the overall dynamics found in the current study show distinguishable characteristics when compared to single wall and unbounded situations.

Edge magnetism in transition metal dichalcogenide nanoribbons: Mean field theory and determinant quantum Monte Carlo

Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is studied using a three-band tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics.

Development of SiC-ZrC-based ultra-high temperature ceramic coatings via composite method of polymer precursor pyrolysis plus gaseous reactive infiltration

SiC-ZrC-based composite coatings on carbon/carbon composites via ZrC polymer precursor pyrolysis (PPP) plus gaseous reactive infiltration (GRI) of Si or ZrSi 2 , separately denoted as GSIC and GZSIC, were comparatively studied to explore the feasibility and effectiveness of GRI of ZrSi 2 . This composite method by applying ZrSi 2 or Si was proven to similarly produce dense coatings with enhanced coating/substrate interfacial bonding strength for the formed zig-zag transition layer. Furthermore, the GRI of ZrSi 2 instead of Si further increased the UHTC (ZrC) content in the as-deposited coatings resulted from the reaction of infiltrated ZrSi 2 and pre-introduced graphite, enhancing the ablation resistance of the coatings for carbon/carbon composites due to the formed stable Zr-rich Zr-Si-O multiphase oxide. The average mass and linear ablation rates were −0.12 mg/s and 1.56 μm/s for GSIC and −0.3 mg/s and −0.53 μm/s for GZSIC specimens, respectively. The average linear ablation rate of the GZSIC specimen was decreased by ~134% when compared to the GSIC specimen. These results further indicate that the PPP + GRI method with metal silicide MeSi 2 (Me = Zr, Ti, Hf, Cr, etc.) will contribute to the optimal fabrication of dense composite coatings with controllable microstructure, adequate evenly-distributed ultra-high temperature ceramic (UHTC) phases, enhanced interfacial bonding strength and wide circumstance suitability for potential applications. The related work is ongoing in our laboratory. • SiC-ZrC-based coatings were made by precursor pyrolysis plus gaseous reactive infiltration. • Pre-introduced graphite reacted with infiltrated ZrSi 2 further improved ZrC content in the coatings. • The gaseous infiltrated ZrSi 2 instead of Si enhanced ablation resistance of the coatings. • The coating's linear ablation rate was reduced by ~134% as gaseous infiltrated with ZrSi 2 .

Homogeneous linear ion crystal in a hybrid potential

We investigate the properties of a linear ion crystal in a combination of quadratic and quartic potentials. Both the discrete and the continuous models are employed to explore the homogeneity of a linear ion crystal by tuning the proportional parameter between the quadratic and quartic components. It is found that the size of the uniform region is significantly larger than that in either a purely quadratic or a quartic potential. The zigzag transition is also investigated in the hybrid potential, and its critical condition and phase diagram are determined numerically, which agrees well with previous theoretical and experimental results. Our results pave the way for experimental investigation of superlarge linear ion crystals in the combination of quadratic and quartic potentials.

Performance and noise prediction of low-Reynolds number propellers using the Lattice-Boltzmann method

This paper proposes a CFD/CAA-based approach to predict the aerodynamic performances and tonal/broadband noise radiation of low-Reynolds number propellers at engineering level. Broadband self-noise prediction of low-Reynolds number propellers is particularly challenging, due to the requirement for the employed computational method to emulate the complexity of the laminar/turbulent boundary-layer behavior on the blade. In this study, the numerical flow solution is obtained by using the Lattice-Boltzmann/Very Large Eddy Simulation method, whereas far-field noise is computed through the Ffowcs-Williams & Hawkings' acoustic analogy applied on the propeller surface. A zig-zag transition trip on the propeller blades is used in the numerical setup to reproduce resolved turbulent pressure fluctuations in boundary-layer for broadband noise computation at a relatively low computational cost. The effect of using a transition trip to simulate low-Reynolds number propellers, as well as the impact of its chordwise position on the calculation of performances and radiated noise, is outlined. The trip position marginally affects the thrust and to a slightly larger extent the torque prediction. Tonal noise at the blade-passing frequencies does not show a relevant sensitivity to it, whereas broadband noise is found to be slightly more influenced by the chordwise position of the trip, especially at high advance ratios. The low sensitivity of the numerical results to the trip location, as well as their good agreement with loads and noise measurements carried out in the A-Tunnel of TU-Delft, demonstrates the robustness of the proposed approach for industrial applications.

Finite-temperature spectrum at the symmetry-breaking linear to zigzag transition

We investigate the normal mode spectrum of a trapped ion chain at the symmetry-breaking linear to zigzag transition and at finite temperatures. For this purpose we modulate the amplitude of the Doppler cooling laser in order to excite and measure mode oscillations. The expected mode softening at the critical point, a signature of the second-order transition, is not observed. Numerical simulations show that this is mainly due to the finite temperature of the chain. Inspection of the trajectories suggest that the thermal shifts of the normal-mode spectrum can be understood by the ions collectively jumping between the two ground state configurations of the symmetry broken phase. We develop an effective analytical model, which allows us to reproduce the low-frequency spectrum as a function of the temperature and close to the transition point. In this model the frequency shift of the soft mode is due to the anharmonic coupling with the high frequency modes of the spectrum, acting as an averaged effective thermal environment. Our study could prove important for implementing ground-state laser cooling close to the critical point.

1D chain structure in 1T′-phase 2D transition metal dichalcogenides and their anisotropic electronic structures

The quasi-metallic 1T'-phase is one of the notable polymorphic two-dimensional transition metal dichalcogenide phases and possesses a unique structure, comprising a one-dimensional zigzag transition metal chain along a single axis. This structure gives rise to unprecedented anisotropic electronic properties, including new anisotropic mid-infrared plasmon excitations. The emergence of highly correlated electronic modes in such anisotropic systems is relevant to the intrinsic electronic and optical properties of two-dimensional transition metal dichalcogenides. In this review, we highlight the unique features of these materials in their anisotropic quasi-metallic 1T'-phase, not found in the other structural phases. We discuss how this anisotropic structure brings about the onset of unique physical phenomena such as the electronic band inversion, anomalously large magnetoresistance, and intrinsic or induced superconductivity in multiple transition metal dichalcogenide systems. The unique structural properties of these systems have led to spatially resolved transport and optical properties that can be further manipulated for use in a wide variety of applications ranging from nano-electronics to ultra-sensitive photonic systems but also their incorporation in high performance field-electric transistors, photodetectors, hydrogen evolution reactions, and piezoelectric devices cater to technologies of the future.

Dinitrogen‐Molybdenum Complex Induces Dinitrogen Cleavage by One‐Electron Oxidation

AbstractReported here is the N2cleavage of a one‐electron oxidation reaction usingtrans‐[Mo(depe)2(N2)2] (1) (depe=Et2PCH2CH2PEt2), which is a classical molybdenum(0)‐dinitrogen complex supported by two bidentate phosphine ligands. The molybdenum(IV) terminal nitride complex [Mo(depe)2N][BArf4] (2) (BArf4=B(3,5‐(CF3)2C6H3)4) is synthesized by the one‐electron oxidation of1upon addition of a mild oxidant, [Cp2Fe][BArf4] (Cp=C5H5), and proceeds by N2cleavage from a MoII‐N=N‐MoIIstructure. In addition, the electrochemical oxidation reaction for1also cleaved the N2ligand to give2. The dimeric Mo complex with a bridging N2is detected by in situ resonance Raman and in situ UV‐vis spectroscopies during the electrochemical oxidation reaction for1. Density‐functional theory (DFT) calculations reveal that the unstable monomeric oxidized MoIspecies is converted into2via the dimeric structure involving a zigzag transition state.

Dinitrogen-Molybdenum Complex Induces Dinitrogen Cleavage by One-Electron Oxidation.

Reported here is the N2 cleavage of a one-electron oxidation reaction using trans-[Mo(depe)2 (N2 )2 ] (1) (depe=Et2 PCH2 CH2 PEt2 ), which is a classical molybdenum(0)-dinitrogen complex supported by two bidentate phosphine ligands. The molybdenum(IV) terminal nitride complex [Mo(depe)2 N][BArf4 ] (2) (BArf4 =B(3,5-(CF3 )2 C6 H3 )4 ) is synthesized by the one-electron oxidation of 1 upon addition of a mild oxidant, [Cp2 Fe][BArf4 ] (Cp=C5 H5 ), and proceeds by N2 cleavage from a MoII -N=N-MoII structure. In addition, the electrochemical oxidation reaction for 1 also cleaved the N2 ligand to give 2. The dimeric Mo complex with a bridging N2 is detected by in situ resonance Raman and in situ UV-vis spectroscopies during the electrochemical oxidation reaction for 1. Density-functional theory (DFT) calculations reveal that the unstable monomeric oxidized MoI species is converted into 2 via the dimeric structure involving a zigzag transition state.

Stability, diffusion and interactions of nonlinear excitations in a many body system

When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.

Ion crystals in anharmonic traps

There is currently intensive research into creating a large-scale quantum computer with trapped ions. It is well known that for a linear ion crystal in a harmonic potential, the ions near the center are more closely spaced compared to the ions near the ends. This is problematic as the number of ions increases. Here, we consider a linear ion crystal in an anharmonic potential that is purely quartic in position. We find that the ions are more evenly spaced compared to the harmonic case. We develop a variational approach to calculate the properties of the ground state. We also characterize the zigzag transition in an anharmonic potential.

Contrasting Structural Reconstructions, Electronic Properties, and Magnetic Orderings along Different Edges of Zigzag Transition Metal Dichalcogenide Nanoribbons.

Two-dimensional transition metal dichalcogenides represent an emerging class of layered materials exhibiting various intriguing properties, and integration of such materials for potential device applications will necessarily invoke further reduction of their dimensionality. Using first-principles approaches, here we investigate the structural, electronic, and magnetic properties along the two different edges of zigzag MX2 (M = Mo, W; X = S, Se) nanoribbons. Along the M edges, we reveal a previously unrecognized but energetically strongly preferred (2 × 1) reconstruction pattern, which is universally operative for all the four systems (and possibly more), characterized by an elegant self-passivation mechanism through place exchanges of the outmost X and M edge atoms. In contrast, the X edges undergo a much milder (2 × 1) or (3 × 1) reconstruction for MoX2 or WX2, respectively. These contrasting structural preferences of the edges can be exploited for controlled fabrication of properly tailored transition metal dichalcogenide nanoribbons under nonequilibrium growth conditions. We further use the zigzag MoX2 nanoribbons to demonstrate that the Mo and X edges possess distinctly different electronic and magnetic properties, which are significant for catalytic and spintronic applications.

Hysteretic and intermittent regimes in the subcritical bifurcation of a quasi-one-dimensional system of interacting particles.

In this article, we study the effects of white Gaussian additive thermal noise on a subcritical pitchfork bifurcation. We consider a quasi-one-dimensional system of particles that are transversally confined, with short-range (non-Coulombic) interactions and periodic boundary conditions in the longitudinal direction. In such systems, there is a structural transition from a linear order to a staggered row, called the zigzag transition. There is a finite range of transverse confinement stiffnesses for which the stable configuration at zero temperature is a localized zigzag pattern surrounded by aligned particles, which evidences the subcriticality of the bifurcation. We show that these configurations remain stable for a wide temperature range. At zero temperature, the transition between a straight line and such localized zigzag patterns is hysteretic. We have studied the influence of thermal noise on the hysteresis loop. Its description is more difficult than at T=0 K since thermally activated jumps between the two configurations always occur and the system cannot stay forever in a unique metastable state. Two different regimes have to be considered according to the temperature value with respect to a critical temperature T_{c}(τ_{obs}) that depends on the observation time τ_{obs}. An hysteresis loop is still observed at low temperature, with a width that decreases as the temperature increases toward T_{c}(τ_{obs}). In contrast, for T>T_{c}(τ_{obs}) the memory of the initial condition is lost by stochastic jumps between the configurations. The study of the mean residence times in each configuration gives a unique opportunity to precisely determine the barrier height that separates the two configurations, without knowing the complete energy landscape of this many-body system. We also show how to reconstruct the hysteresis loop that would exist at T=0 K from high-temperature simulations.

Subcriticality of the zigzag transition: A nonlinear bifurcation analysis.

When repelling particles are confined by a transverse potential in quasi-one-dimensional geometry, the straight line equilibrium configuration becomes unstable at small confinement, in favor of a staggered row that may be inhomogeneous or homogeneous. This conformational phase transition is a pitchfork bifurcation called the zigzag transition. We study the zigzag transition in infinite and periodic finite systems with short-range interactions. We provide numerical evidence that in this case the bifurcation is subcritical since it exhibits phase coexistence and hysteretic behavior. The physical mechanism responsible for the change in the bifurcation character is the nonlinear coupling between the transverse soft mode at the transition and the longitudinal Goldstone mode linked to the translational or rotational invariance of the zigzag pattern. An asymptotic analysis, near the bifurcation threshold and assuming an infinite system, gives an explicit expression for the normal form of the bifurcation. We establish the subcriticality, and we describe with excellent precision the inhomogeneous zigzag patterns observed in the simulations. A direct test of the physical mechanism responsible for the bifurcation character evidences a quantitative agreement.

Longitudinal and Transverse Single File Diffusion in Quasi-1D Systems

We review our recent results on Single File Diffusion (SFD) of a chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We exhibit new behaviors specifically associated to small systems and to small damping. The fluctuation dynamics is explained by the decomposition of the particles' motion in the normal modes of the chain. For longitudinal fluctuations, we emphasize the relevance of the soft mode linked to the translational invariance of the system to the long time SFD behavior. We show that close to the zigzag threshold, the transverse fluctuations also exhibit the SFD behavior, characterized by a mean square displacement that increases as the square root of time. This cannot be explained by the single file ordering, and the SFD behavior results from the strong correlation of the transverse displacements of neighbouring particles near the bifurcation. Extending our analytical modelization, we demonstrate the existence of this subdiffusive regime near the zigzag transition, in the thermodynamic limit. The zigzag transition is a supercritical pitchfork bifurcation, and we show that the transverse SFD behavior is closely linked to the vanishing of the frequency of the zigzag transverse mode at the bifurcation threshold. [Formula: see text] Special Issue Comments: This article presents mathematical results on the dynamics in files with longitudinal movements. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics,28 expanding files,63 and files with force and advanced formulations.29

Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap

The Coulomb repulsion between ions in a linear Paul trap gives rise to anharmonic terms in the potential energy when expanded about the equilibrium positions. We examine the effect of these anharmonic terms on the accuracy of a quantum simulator made from trapped ions. To be concrete, we consider a linear chain of ${\text{Yb}}^{171+}$ ions stabilized close to the zigzag transition. We find that for typical experimental temperatures, frequencies change by no more than a factor of $0.01%$ due to the anharmonic couplings. Furthermore, shifts in the effective spin-spin interactions (driven by a spin-dependent optical dipole force) are also, in general, less than $0.01%$ for detunings to the blue of the transverse center-of-mass frequency. However, detuning the spin interactions near other frequencies can lead to non-negligible anharmonic contributions to the effective spin-spin interactions. We also examine an odd behavior exhibited by the harmonic spin-spin interactions for a range of intermediate detunings, where nearest-neighbor spins with a larger spatial separation on the ion chain interact more strongly than nearest neighbors with a smaller spatial separation.

Magnetic Exchange Coupling and Anisotropy of 3d Transition Metal Nanowires on Graphyne

Applying two-dimensional monolayer materials in nanoelectronics and spintronics is hindered by a lack of ordered and separately distributed spin structures. We investigate the electronic and magnetic properties of one-dimensional zigzag and armchair 3d transition metal (TM) nanowires on graphyne (GY), using density functional theory plus Hubbard U (DFT + U). The 3d TM nanowires are formed on graphyne (GY) surfaces. TM atoms separately and regularly embed within GY, achieving long-range magnetic spin ordering. TM exchange coupling of the zigzag and armchair nanowires is mediated by sp-hybridized carbon, and results in long-range magnetic order and magnetic anisotropy. The magnetic coupling mechanism is explained by competition between through-bond and through-space interactions derived from superexchange. These results aid the realization of GY in spintronics.

A strongly coupled zig-zag transition

Abstract The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.